Crystal structure of trirubidium citrate from laboratory X-ray powder diffraction data and DFT comparison

The crystal structure of trirubidium citrate has been solved and refined using laboratory X-ray powder diffraction data, and optimized using density functional techniques.


Structural commentary
The asymmetric unit of the title compound is shown in Fig. 1. The root-mean-square deviation of the non-hydrogen atoms in the Rietveld-refined and DFT-optimized structures is 0.052 Å (Fig. 2). The largest difference is 0.086 Å , at C1. The excellent agreement between the two structures is strong evidence that the experimental structure is correct (van de Streek & Neumann, 2014). This discussion uses the DFT-optimized structure. Most of the bond lengths, bond angles, and torsion angles fall within the normal ranges indicated by a Mercury Mogul geometry check (Macrae et al., 2008). The C3-C2-C1 angle of 116.5 is flagged as unusual [Z-score = 2.3; average = 112.7 (16) ]. The C2-C3-C2 angle of 106.0 is also flagged as unusual [Z-score = 2.5; average = 109. 6 (14) ]. This hygroscopic compound was measured in situ, so perhaps slightly unusual geometry could be expected.
The citrate anion occurs in the trans,trans-conformation, which is one of the two low-energy conformations of an isolated citrate. The central carboxylate group and the hy-droxy group lie on a mirror plane. The terminal carboxylate O11 atom and the central carboxylate O15 atom chelate to Rb19, O11 and the central carboxylate O16 atom chelate to a second Rb19, and the terminal carboxylate O12 atom and the O17 hydroxy group chelate to a third Rb19. The terminal O11-C1-C12 carboxylate group acts as a bidentate ligand to Rb20. The Mulliken overlap populations and atomic charges indicate that the metal-oxygen bonding is ionic.
The Bravais-Friedel-Donnay-Harker (Bravais, 1866;Friedel, 1907;Donnay & Harker, 1937) morphology suggests that we might expect blocky morphology for trirubidium citrate, with {011} as the principal faces. A 4th-order spherical harmonic texture model was included in the refinement. The texture index was 1.001, indicating that preferred orientation was not significant for this rotated flat-plate specimen.

Supramolecular features
The two independent Rb + cations, Rb19 and Rb20, are sevenand eight-coordinate, with bond-valence sums of 0.99 and 0.92 valence units, respectively. The coordination polyhedra share edges and corners to form a three-dimensional network (Fig. 3). The only hydrogen bond is an intramolecular one (Table 1)  The asymmetric unit of trirubidium citrate, showing the atom numbering. The atoms are represented by 50% probability spheroids.

Figure 2
Comparison of the refined and optimized structures of trirubidium citrate. The refined structure is in red, and the DFT-optimized structure is in blue.

Figure 3
Crystal structure of trirubidium citrate, viewed down the b axis. Table 1 Hydrogen-bond geometry (Å , ) for ramm077c_DFT. population indicates, by the correlation in Rammohan & Kaduk (2017a), that this hydrogen bond contributes 12.6 kcal mol À1 to the crystal energy.

Database survey
Details of the comprehensive literature search for citrate structures are presented in Rammohan & Kaduk (2017a). A reduced cell search of the cell of trirubidium citrate monohydrate in the Cambridge Structural Database (Groom et al., 2016) (increasing the default tolerance from 1.5 to 2.0%) yielded 221 hits, but combining the cell search with the elements C, H, O, and Rb only yielded no hits.

Synthesis and crystallization
A portion of Rb 3 (C 6 H 5 O 7 )(H 2 O) 1 (Rammohan & Kaduk, 2017c) was heated at 14 K min À1 to 463 K and held at that temperature for 10 min. The white solid was immediately transferred to a glass vial to cool.

Refinement
Crystal data, data collection and structure refinement details are summarized in Table 2. Diffraction data are displayed in Fig. 4. The white solid was ground in a mortar and pestle, blended with NIST 640b Si internal standard in order to verify the calibrated goniometer zero error, packed into a standard Bruker D2 sample cell and protected from the atmosphere by an 8 mm thick Kapton window attached to the cell with Vaseline. The powder pattern indicated that the sample was still hydrated, so the blend was re-heated at 17 K min À1 to 483 (10) K and held for 10 min. Re-measuring the powder pattern indicated that a new phase had formed. The pattern was indexed using DICVOL06 (Louë r & Boultif, 2007) on a primitive orthorhombic cell having a = 7.904, b = 12.701, c = 10.773 Å , and V = 1081.8 Å 3 . These lattice parameters are 2.6, 1.8, and 3.3% larger than those of K 3 C 6 H 5 O 7 (Rammohan & Kaduk, 2016e), and the volume is 7.9% larger. The compound was assumed to be isostructural to the K analogue (space group Pna2 1 ), and the coordinates of tripotassium citrate were used as the initial model for the Rietveld refinement.
Pseudo-Voigt profile coefficients were as parameterized in Thompson et al. (1987) with profile coefficients for Simpson's rule integration of the pseudo-Voigt function according to Howard (1982). The asymmetry correction of Finger et al. (1994) was applied, and microstrain broadening by Stephens (1999). The structure was refined by the Rietveld method using GSAS/EXPGUI (Larson & Von Dreele, 2004;Toby, 2001). All C-C and C-O bond lengths were restrained, as were all bond angles. The hydrogen atoms were included at fixed positions, which were recalculated during the course of the refinement using Materials Studio (Dassault Systè mes, 2014). The U iso value of the C atom in the central part of the citrate anion, and the C and O atoms on the exterior, were constrained to be equal, and the U iso valuess of the hydrogen atoms were constrained to be 1.3 times those of the atoms to which they are attached.

Figure 4
Rietveld plot for the refinement of trirubidium citrate. The vertical scale is not the raw counts but the counts multiplied by the least-squares weights. This plot emphasizes the fit of the weaker peaks. The red crosses represent the observed data points, and the green line is the calculated pattern. The magenta curve is the difference pattern, plotted at the same scale as the other patterns. The row of black tick marks indicates the reflection positions. The red tick marks indicate the positions of the peaks of the Si internal standard.
module of PLATON (Spek, 2009) and the Find Symmetry module of Materials Studio (Dassault Systè mes, 2014) suggested the presence of an additional centre of symmetry, and that the space group was Pnma (with a transformation of axes). The tolerance on the search was 0.12 Å . Because lower residuals were obtained with fewer parameters, we believe that Pnma is the correct space group.

DFT calculations
After the Rietveld refinement, a density functional geometry optimization (fixed experimental unit cell) was carried out using CRYSTAL14 (Dovesi et al., 2014). The basis sets for the C, H, and O atoms were those of Peintinger et al. (2012), and the basis set for Rb was that of Schoenes et al. (2008). The calculation was run on eight 2.1 GHz Xeon cores (each with 6 Gb RAM) of a 304-core Dell Linux cluster at IIT, used 8 kpoints and the B3LYP functional, and took about seven h. The U iso values from the Rietveld refinement were assigned to the optimized fractional coordinates.